The Saleemi Corporation's $1,000 bonds pay 14 percent interest annually and have 18 years until maturity....

 

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The Saleemi Corporation's $1,000 bonds pay 14 percent interest annually and have 18 years until maturity. You can purchase the bond for $1,160. a. What is the yield to maturity on this bond? b. Should you purchase the bond if the yield to maturity on a comparable-risk bond is 13 percent? a. The Saleemi Corporation's $1,000 bonds pay 14 percent interest annually and have 18 years until maturity. You can purchase the bond for $1,160. What is the yield to maturity on this bond? STEP 1: Picture the problem The cash flows for the bond consist of the purchase price for the bond today of $1,160, annual interest payments for years 1 through 17 of $140, and a final interest plus principal payment of $1,000 at the end of year 18 equal to $1,140. YTM=?% Time Period 0 2 Cash Flow -$1,160 $140 $140 STEP 2: Decide on a solution strategy 17 18 years + $140 $1,140 To solve for the bond's yield to maturity we can use a mathematical equation to find YTM, which is the rate of interest to discount the cash flows paid to the bondholder in years 1 through 18 that makes the present value equal to the current market price of $1,160. We can do this the same three ways that we solved time value of money problems involving multiple cash flows. That is, mathematically, using a calculator, and using a spreadsheet. STEP 3: Solve Using a Mathematical Formula. It is cumbersome to solve for the yield to maturity by hand using a mathematical formula except in very special cases. For example, substituting the numbers for the bond into the following equation where the term to maturity is 18 years, we get the following result: Styear 2 (1+ YTM2 Interest Bond Price = tyear 1 (1+ YTM)1 Interest Interest year 18 (1+YTM)18 Principal (1+ YTM)18 $140 $140 $140 $1,000 $1,160 = + + (1+ YTM)1 (1+ YTM) (1+ YTM)18 (1+ YTM)18 Note that to keep from having to write out all 18 years of interest payments we have simply added "..." to reflect the omitted terms for years 3 through 17. This would be a tough equation to solve mathematically since the variable we are solving for, YTM, is raised to powers ranging from 1 to 18. For this reason, investors and financial managers use either a financial calculator or Excel to calculate the yield to maturity. Using a Financial Calculator. Enter 18 - 1,160 N I/Y PV 140 PMT 1,000 FV Solve for 11.82% Thus, the yield to maturity on the bond is 11.82%. Notice, the value of the bond, PV, is input with a negative sign since the purchase price of the bond is seen by both the financial calculator and Excel as a cash outflow. Using an Excel Spreadsheet. =RATE(nper,pmt,pv,fv) or with values entered = RATE(18,140,- 1160,1000) b. STEP 4: Analyze The value of a bond is inversely related to changes in the yield to maturity. Since your yield to maturity on the Saleemi bonds is less than the yield to maturity on a comparable-risk bond, the Saleemi bonds are overpriced and thus you should not purchase the bonds and earn a lower rate of return. The Saleemi Corporation's $1,000 bonds pay 14 percent interest annually and have 18 years until maturity. You can purchase the bond for $1,160. a. What is the yield to maturity on this bond? b. Should you purchase the bond if the yield to maturity on a comparable-risk bond is 13 percent? a. The Saleemi Corporation's $1,000 bonds pay 14 percent interest annually and have 18 years until maturity. You can purchase the bond for $1,160. What is the yield to maturity on this bond? STEP 1: Picture the problem The cash flows for the bond consist of the purchase price for the bond today of $1,160, annual interest payments for years 1 through 17 of $140, and a final interest plus principal payment of $1,000 at the end of year 18 equal to $1,140. YTM=?% Time Period 0 2 Cash Flow -$1,160 $140 $140 STEP 2: Decide on a solution strategy 17 18 years + $140 $1,140 To solve for the bond's yield to maturity we can use a mathematical equation to find YTM, which is the rate of interest to discount the cash flows paid to the bondholder in years 1 through 18 that makes the present value equal to the current market price of $1,160. We can do this the same three ways that we solved time value of money problems involving multiple cash flows. That is, mathematically, using a calculator, and using a spreadsheet. STEP 3: Solve Using a Mathematical Formula. It is cumbersome to solve for the yield to maturity by hand using a mathematical formula except in very special cases. For example, substituting the numbers for the bond into the following equation where the term to maturity is 18 years, we get the following result: Styear 2 (1+ YTM2 Interest Bond Price = tyear 1 (1+ YTM)1 Interest Interest year 18 (1+YTM)18 Principal (1+ YTM)18 $140 $140 $140 $1,000 $1,160 = + + (1+ YTM)1 (1+ YTM) (1+ YTM)18 (1+ YTM)18 Note that to keep from having to write out all 18 years of interest payments we have simply added "..." to reflect the omitted terms for years 3 through 17. This would be a tough equation to solve mathematically since the variable we are solving for, YTM, is raised to powers ranging from 1 to 18. For this reason, investors and financial managers use either a financial calculator or Excel to calculate the yield to maturity. Using a Financial Calculator. Enter 18 - 1,160 N I/Y PV 140 PMT 1,000 FV Solve for 11.82% Thus, the yield to maturity on the bond is 11.82%. Notice, the value of the bond, PV, is input with a negative sign since the purchase price of the bond is seen by both the financial calculator and Excel as a cash outflow. Using an Excel Spreadsheet. =RATE(nper,pmt,pv,fv) or with values entered = RATE(18,140,- 1160,1000) b. STEP 4: Analyze The value of a bond is inversely related to changes in the yield to maturity. Since your yield to maturity on the Saleemi bonds is less than the yield to maturity on a comparable-risk bond, the Saleemi bonds are overpriced and thus you should not purchase the bonds and earn a lower rate of return.